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Fine-Tuning Excludes the Multiverse Hypothesis and Confirms Coherent Cosmology, Eddington's and String Theories F

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Fine-Tuning Excludes the Multiverse Hypothesis and Confirms Coherent Cosmology, Eddington's and String Theories F Fine-tuning excludes the Multiverse Hypothesis and confirms Coherent Cosmology, Eddington's and String Theories F. M. Sanchez, M. Grosmann, D. Veigel, R. Veysseyre, C. Bizouard, D. Gayral, L. Gueroult Fine tuning relations using Eddington number 137 and the central mathematical constants e, π, γ connect with the Fermi coupling constant, the muon and tau masses, and the G value. The latter is compatible, within 10-7 with the G value deduced from the Coherent Cosmology, and within 10-9 to the electron magnetic moment. The formula simplify by introducing a super Euler - constant, and show a 9D reduction to 3D, confirming Superstring Theory, while c-free analysis confirms the Topological Axis and the tachyonic Bosonic String Theory, with emphasis on a 30 dimension Space, connected through triple Bott reduction with a massive Gluon in 6 dimension space. The 26 sporadic groups are tied to the three microphysics coupling constant and the gauge group dimension 496, whose square give the Higgs boson/Electron mass ratio. The Baby-Monster is directly tied to the observable Universe. The Monster Group, whose cardinal order is directly tied to Rydbergh energy (10-6) appears in the c-free analysis giving the overall periodicity of a Deterministic Grandcosmos Computer. This confirms the exclusion of the Multiverse hypothesis and Eddington's rehabilitation. The Eddington's number 137 has a fundamental property: it appears as a Monster Prime in the series of the maximal primes appearing in the numerator of the harmonic series: 3,11,5,137,7,11, showing a symmetry between the 11 supergravity dimensions and the 4 of space-time: 137 = 11² + 4² Since Riemann series are tied to the prime number distribution, it is strange that mathematicians have not point out the primes appearing in the Harmonic series, since it is the single pole. It seems that the basic precept 'all occurs in the pole' was forgotten in this case. As ancient Egyptian used only fractions of type 1/n, they were certainly aware of this particular number 137. Indeed the fifth harmonic series s5 = 137/60 appears in the Ptolemaic approximation for π: 377/120 = 2 + s5/2. Recall that the electrical constant characterizes the force ħc/al² between two l - distant elementary charges, appearing central in Atomic Physics and in many fine-tuning relations [2]. It is strange that physicists focused on only one property, the appearance of its fifth power in the Hydrogen hyper-fine spectra, and call its inverse the 'fine-structure constant'. It is strange also that Eddington's Theory was rejected as soon as a appeared to be different from 137. The present article shows that 137 plays a central role in fine-tuning analysis. Indeed a simple computer study shows that 137 and the Euler-Mascheroni constant γ enter the relation: 2 3 GF/mec ≈ (πƛe/2γ137a) 3 -62 where ƛe ≡ ħ/mec is the reduced electron radius, and GF ≡ (ħc) /EF ² ≈ 1.4358509(7) ×10 Joule × 3 2 m is the Fermi coupling constant, corresponding to the Fermi energy EF = Fmec ≈ 292.806161(6) 2 GeV ≈ 573007.33(25) mec [3]. 2 -7 Admitting the above relation, this defines F = EF/mec ≈ 573007.3652, inside its 2.5 10 indetermination. Now the latter enters another fine tuning relation, induced by the Kotov Coherent 2 Cosmic Oscillation [4], implying the muon, proton and Hydrogen masses: EF/mec ≈ 2 3 -8 mµ √(mpmH)/ame . This corresponds to a muon mass 206.7682869 me, inside its 2 × 10 measurement range. The a-priori probability of such correlations are estimated, by looking for the number of solutions obtained by extending the indetermination range by a factor 106, keeping a maximal exponent to 3, to be respectively 2 × 10-5 and 10-6. From the Koide relation [5], one gets the corresponding mass ratio tau/electron: τ ≈ 3477.441701, see below. Fine-tuning research also show that the most elegant formula for the strong coupling constant is [4] 3/2 f ≡ aw/2π(pH) ≈ 8.434502892 while the CODATA value is badly defined fCODATA ≈ 1/0.1181(11). With 496, the dimension of the gauge group of type 1 string theory, one notes, to 0.05 % : F/af ≈ 496 The importance of this Central Relation between the three microscopic coupling constant will be confirmed later, in connexion with the sporadic groups. Note that the mass ratio scalar Higgs Boson/electron is close to: s ≈ 196² corresponding to 125.7 GeV, while the experimental value is 125.09(24) GeV. Now, the three first terms of the Combinatorial Hierarchy [6] are the connected Mersenne numbers 3, 7, 127, whose sum is 137, so giving the first order of the electrical constant. The following (final) term 2127-1, the most famous prime in number theory, gives the first order of the gravitational coupling, whose optimal form results from the gravitational Hydrogen molecule model [7] aG = ħc/GmpmH. Computer analysis shows the following symmetrical expression for the deviation, with n ≈ 1838.68366089(17) the neutron/electron mass ratio: 127 1/2 4 3 (2 /aG) ≈ F(a/π) (γ /4n) this corresponds to G ≈ 6.675453818 × 10-11 kg-1m3s-2 compatible within 10-7 with the value deduced from Coherent cosmology [7]. It is compatible with the well-elaborate 10-5 BIPM measurement [8], but at several sigmas from the Codata value, since the later is the mean between discordant measurements. A secular variation of G with a terrestrial period has been suggested, but not consistent with the phases. The formula exhibits a symmetry between a and π. In this respect one notes that, to 2 ×10-7: a² ≈ 137² + π², and that, by analogy with the Euler formula: i-ilni = exp(π²/2) ≈ √(a+2), and the first -ilni -9 development term of de, with u = i √a -1, one obtains a within 3 × 10 : a ≈ u - 1/2πu = 137.035999548 Moreover, one obtains a value a ≈ 137.035999119 compatible with measurement a ≈ 137.035999139(31) in : 2 ln137/ln(a/137) ≈ (2+135/de) with de ≈ 1.00115965218091(26), the anomalous electron magnetic moment, meaning the ratio a/137 shows a type of musical role. Now, with the above value of G, the mass ratio proton-electron p ≈ 1836.15267389(17) and the mass ratio Hydrogen-electron H ≈ 1837.15264726(17), the computer indicates a 10-9 correlation: 127 1/2 3 (2 /aG) ≈ de(H/p) This writes: 1/3 (aF/πde ) ≈ 4πn'/γ a where n' = nH/p is the principal value of the neutron mass by respect to the electron effective mass in the Hydrogen atom. Note the 0.12 % proximity of the above number with the fifth fractional development of π: 292.6345909, itself approaching n/2π to 3.4 10-6. By introducing a super-Euler constant : Γ = γ a/π the relation giving GF becomes much simpler: 2 3 GF/mec ≈ (ƛe/137×2Γ ) and the above relation giving aG shows a double form: 127 1/2 2 3 -3 3 -1 (2 /aG) ≈ (a/π)(nF/137 Γ ) ≈ (a/π)((4n/Γ) /F) corresponding to a dimensional reduction, by eliminating 137, from 9D and 6D to 3D, which could be associated to Superstring theory, where the equations are coherent only if space has 9 dimensions, and if the 6 supplementary dimensions are fold on very small distances. The above tau number enters the following much symmetrical relation, to 1.5 ×10-6: (τ²Γ / a²)3 ≈ 4pnH (496(H-p)/137)4 calling for further analysis. Such relations are unbelievable for reductionist people, arguing that since neutron is composite, it cannot enter simple relations. The same argument is presented for the theoretical dependence of a with other constants g and g'. But Coherent Cosmology [7] shows that the holistic point of view is more pertinent than the classical reductionnist one. Moreover, both the number 137 and the term aa appear in musical number analysis [9], confirming that a is an optimal calculation basis. Such transcendental formulas are surprising for theorists which forget that beauty is the root of Science. In particular, the famous Lucas-Lehmer primality test uses the series of whole numbers Nn+1 = Nn² – 2, starting from N = 4 = u3 + 1/u3, with u3 = √3 + 2, belonging to the Diophantine generators un = √n + √(n+1). One shows that Nn ≈ u3^(2^q), and for q = 9: 64 a u3^(2^9) ≈ (2×(a² + 2√µ)) ≈ a defining a to 39 ppm, where µ is the mass ratio muon/electron and the main term 2a² = mec²/ERyd is tied to the Rydbergh energy's principal value ERyd whose ratio with the Planck energy is closely related to the Monster group cardinal order, to 1.5 × 10-6: -1///2a 5 2 OM e ≈ (EP/ERyd)² = ħGc /ERyd See below the incredible other properties of OM. Also, with the Pell-Fermat generator u1 = 1 + √2: a 8 a ≈ u1^(3×(2 - 1)) a defining a to 0.3 ppm. So the number a establishes a connexion between u1 and u3, two of the simplest arithmetics generators. This opens a new research in pure mathematics. The number π appears as a calculation basis in the Riemann series of even order. So, it is natural to consider the ratio π/e. Note that, with 34, the number of primes leading to 137 (by counting 1 as a prime number) the Bohr atomic radius writes, to 1.4 × 10-6: 34 rH = a ƛe(1+1/p) ≈ (H-p) (π/e) This leads to the discovery of the incredible relation: 3 1/2 p (2/3)(2aG) ≈ (a/137) (π/e) -8 which confirms the above G value to 4 × 10 .
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